The War on Algebra

Unfortunately, the misguided transformation of algebra into a course for the masses has proven to be a cure worse than the disease. The transformation has resulted in a less rigorous course. Introductory textbooks have slimmed down considerably over the past century, omitting some subjects entirely. The primary victims of this dumbing-down are the elite students themselves. Among the most recent cohorts of college graduates, the proportion of male students majoring in math-intensive subjects has continued to hover in the 20% range. If we compare this to the historical 30% rate of two generations ago, we lose about 100,000 mathematicians, scientists, and engineers every year – enough to replace every American employee of both Microsoft and Google and still have tens of thousands to spare.

Algebra remains a course that is simply too difficult for many students. With Duke colleagues Charles Clotfelter and Helen Ladd, I’ve recently conducted an evaluation of an algebra acceleration initiative that occurred about 10 years ago in the Charlotte-Mecklenburg school system. Students placed into algebra a year early ended up significantly less likely to complete a three-course college prep math curriculum – Algebra I, Geometry, and Algebra II by the time they completed high school.

So, in a nutshell, we have the story of Americas’ twin mathematics problems. Begin with a focus on inequality, and a mistaken premise that everyone could be another Einstein if they just have access to the right courses at the right time. You’ll soon be patting yourself on the back for closing the gap between the best and the worst, only occasionally reminded that neither your best nor worst students are doing all that well in absolute terms. You’ve fallen into what might be termed the “achievement gap trap.”

Unless I misunderstand what he’s writing, he’s advocating a tracking system along the lines of those commonplace elsewhere in the world in which preadolescents are assigned to specific academic tracks suitable to the roles they will fill later in life. “Elite” students who will go on to university take the more intellectually demanding courses, others are spared those courses and will become laborers or factory workers or members of the trades.

I have no idea how that system works in Germany or the United Kingdom or Singapore and, honestly, I don’t care. We have our own social conditions and I have pretty fair confidence on how such a system would work out here. Black and Hispanic students would routinely be deemed not appropriate material for more academically challenging courses. Kids whose dads were physicians or lawyers or bankers or whose dads owned big software companies, most of whom these days don’t live in the same neighborhoods or attend the same schools as kids whose parents aren’t in the upper income brackets, would be assumed to be appropriate for such material. Regardless of actual ability kids with better backgrounds would be “elite”; kids who weren’t would be tracked into non-academically challenging subjects which, essentially, did not lead to higher education. Kids with special educational needs would be warehoused. Unless, of course, their parents were lawyers or doctors or bankers or owned big software companies. In that case they’d receive every resource the public education system could offer.

Or, said another way, it would be system that prevailed here in the 1940s.

There’s one other thing in the article I’d like to comment on. This:

The pragmatic attitude towards mathematics for the masses gave way in the post-World War II era. Successive waves of curricular reforms sought to improve the mathematical skills of ordinary students. The “New Math” movement of the 1950s and early ‘60s tried to beef up the curriculum for all students, with disastrous results. By steering the curriculum away from practical application to a focus on fundamentals, new math managed to turn a generation of students off from math. Male college graduates raised in the new math era chose math-intensive majors at a rate of 20% — down a third relative to the prior generation.

is essentially hooey. What actually happened is that in the late 60s and early 70s the space program was wound down, engineering jobs became much harder to find, and the NSF cut funding for science and math education. “Progressive education” assumed increasing influence. Here’s a quote from the influential book, Summerhill, the bible of that movement, which should give you the general idea:

Whether a school has or has not a special method for teaching long division is of no significance, for long division is of no importance except to those who want to learn it. And the child who wants to learn long division will learn it no matter how it is taught.

Summerhill was required reading in many education programs in the 1970s. The people who took those programs are running school systems today.

I’m getting old and senile. I can’t remember who said what to whom in these threads.

But there was an algebra discussion recently. Someone made the, correct in my opinion, observation that math, specifically algebra, was just a mind exercise. Even if you never used it in real life. I say the same about calculus.

I do remember making the observation that I’d take statistical understanding over other mathematical endeavors as a practical matter. I still feel that way. But I don’t want to overly discount the value of mathematical training, in which, apparently, a frequent commenter is formally trained. It is a wonderful way to exercise and train the mind.

I don’t care if you can’t really remember what Greens theorem is all about 1 or 2 years out of college. It just matters that you had to grapple with it at some point.

I don’t think that tracking towards the trades vs university really changes the basic notion of grounding in a thinking style.

Looking at the Charlotte-Mecklenburg study, I find this conclusion: “Our empirical evidence, based on a clear policy intervention affecting nearly the entire distribution of students in one of the nation’s largest school districts avoids the selection bias, and shows that early administration of Algebra I –
when not preceded by a longer-run strategy to accelerate the math curriculum – is actually harmful for success in math.” (emphais in original)

@Drew, I believe you are referring to Odograph, though I don’t think his argument was clearly presented at first. The referenced study states its as follows: “From an economic perspective, algebra skills can be valued for two basic reasons. First, algebra skills may contribute directly to labor productivity. Second, algebra skills might serve as inputs into the production of higher-order mathematical knowledge, which in turn may have an independent effect on productivity.”

I remember Algebra being the first real abstract math without a lot of obvious real world examples. I ended up taking Physics before Trig (and doing vector addition the hard way with a ruler and protractor). When I came around to learning Trig it was much more appreciated. Anyway, all this to say I think that a concrete introduction can make someone appreciate the abstract method, rather than just an accelerated curriculum.
For instance, when I took my private pilot course, I think a few of the students who learned to do wind calculations with an E6B would have been more interested in trig afterward.

“I have no idea how that system works in Germany or the United Kingdom or Singapore and, honestly, I don’t care. We have our own social conditions and I have pretty fair confidence on how such a system would work out here. Black and Hispanic students would routinely be deemed not appropriate material for more academically challenging courses. Kids whose dads were physicians or lawyers or bankers or whose dads owned big software companies, most of whom these days don’t live in the same neighborhoods or attend the same schools as kids whose parents aren’t in the upper income brackets, would be assumed to be appropriate for such material. Regardless of actual ability kids with better backgrounds would be “elite”; kids who weren’t would be tracked into non-academically challenging subjects which, essentially, did not lead to higher education. Kids with special educational needs would be warehoused. Unless, of course, their parents were lawyers or doctors or bankers or owned big software companies. In that case they’d receive every resource the public education system could offer.

Or, said another way, it would be system that prevailed here in the 1940s.”

Dave, if you throw in politically connected contractors running schools or selling standardized tests at high profits here you would have a perfect summary of the objectives of corporate ed reform being pushed by Penny Pritzker, Rahm, Arne Duncan, Bill Gates, Bloomberg, Joel Klein and the Koch brothers.

Yet again our school systems are pandering to the lowest common denominator, as opposed to pulling the student up to a higher standard. Sad.

Progressive-style education must be filtered through Marxist ideology, in my opinion. Consider this quote from Karl Marx:

“The less you eat, drink and read books; the less you go to the theatre, the dance hall, the public house; the less you think, love, theorize, sing, paint, fence, etc., the more you save-the greater becomes your treasure which neither moths nor dust will devour-your capital. The less you are, the more you have; the less you express your own life, the greater is your alienated life-the greater is the store of your estranged being.” –Karl Marx

Marx believed one should be able to do whatever they want, whenever they want, however they want–capricious will. Sounds like “progressive education” to me. Imagination trumps logic, as opposed to the other way around. It is all upside down if you ask me.

I know one thing: you better understand algebra if you hope to major in computer science (lots of math); and we all know how much the kids love their computers and other tech thingies.